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| 摘要: |
| 本文改进了基于MUSCL方法求解一维浅水波方程组的中心迎风格式.利用MUSCL-Hancock方法在每个时间步的中间时刻求解Riemann问题，并分别在tn时刻和tn+1/2时刻对自由面的斜率进行了修正，得到了MUSCL-Hancock中心迎风格式.在合理的CFL条件下，我们证明了该格式的平衡性与保正性.数值结果表明，与MUSCL格式相比，本文格式能有效减少计算量并具有更高的分辨率. |
| 关键词: 浅水波方程组 MUSCL-Hancock中心迎风格式 保正性 平衡性 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家自然科学基金资助（11371023）. |
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| A WELL-BALANCED POSITIVITY PRESERVING MUSCL-HANCOCK CENTRAL-UPWIND SCHEME FOR SHALLOW WATER EQUATIONS WITH TOPOGRAPHY |
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WANG Jing-zhou,TONG Wei,YAN Rui-fang,CHEN Guo-xian
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| Abstract: |
| In this paper, we improve the central-upwind scheme for solving one-dimensional shallow water wave equations based on MUSCL method. This method adopted MUSCL-Hacock method to solve the Riemann problem at the middle of each time step, and correct the slope of the free surface at tn and tn+1/2 respectively, which is called MUSCL-Hancock central-upwaind scheme. Under the reasonable CFL condition, we prove that the new scheme is well-balanced and preserves non-negativity of the water height. Compared with MUSCL scheme,numerical examples show that the method can effectively reduce computation and has higher resolution. |
| Key words: shallow water equations MUSCL-Hancock central-upwind scheme positivity preserving property well-balanced property |
